HEXAGONAL MARANGONI CONVECTION IN A RECTANGULAR BOX WITH SLIPPERY WALLS

A linear and nonlinear study of surface-tension-driven instability in a rectangular box with slippery lateral walls is presented. Particular attention is devoted to steady convection with hexagonal structure. I t is shown that, even in very small boxes, convection can set in in th e form of hexagons more or less distorted according to the aspect rati os of the box. The distorted hexagons appear generally as subcritical solutions; the depth of the subcritical domain is determined as a func tion of the Prandtl number. In particular, it is found that, at small Prandtl numbers (Pr less-than-or-equal-to 0.23), the direction of the flow may be downwards at the cell centre. For medium to large values o f the Prandtl number, the fluid rises at the centre of the hexagons, a s is observed in most experiments.